Given:
length of the radius = 4
Circle centered at origin
To find:
the equation of the circle
To determine the equation of the circle, we will apply the formula:
[tex]\begin{gathered} (x\text{ - h\rparen}^2+\text{ \lparen y - k\rparen}^2\text{ = r}^2 \\ where\text{ \lparen h, k\rparen is the center of the circle} \\ r\text{ = radius} \end{gathered}[/tex]Since the circle is from the origin, the center will be (0, 0)
[tex]\begin{gathered} h\text{ = 0} \\ k\text{ = 0} \\ r\text{ = 4} \\ \\ substitute\text{ the values:} \\ (x\text{ - 0\rparen}^2\text{ + \lparen y - 0\rparen}^2\text{ = 4}^2 \\ \\ The\text{ equation of the circle:} \\ x^2\text{ + y}^2\text{ = 4}^2\text{ \lparen option C\rparen} \end{gathered}[/tex]